Major John J. Kelly, Chief of the Training Divisionof II Army Corps, was found dead of a gunshot wound in the head here yesterday at Miller Field, New Dorp, Staten Island.

Army authorities said a .38 caliber pistol was lying near his right hand. The Army and Federal Bureau of Investigation began inquiries.

Major Kelly, the 45-year-olf, father of four childrem, lived at Miller Field, an Army Base. He was stationed at Fort Wadsworth, about five miles away, where II Corps has headquarters.